The Edmund Williams who married Caroline appears to have been son of a Registrar, so should have known how to write his own name. Maybe the "Edward" on the 1901 census was the enumerator's error.
1861 Church St, Malpas RG9/1891 ED1 FOL10 PG14
John Williams, Head, Mar, 45, Registrar of Births & Deaths & Spirit Vaults, Cheshire Malpas
Arabella do, Wife, Mar, 37, , do Neston
Mary Ann do, Daur, un, 16, Daur, do Malpas
Elizabeth do, Daur, un, 14, Scholar, do do
Alice do, Daur, , 13, do, do do
Robert do, Son, , 11, do, do do
Catharine do, Daur, , 8, do, do do
George Fredk do, Son, , 6, do, do do
Edmund Alfred Bulkeley do, Son, 4, do, do do
1871 Church Street, Malpas RG10/2798 ED1 FOL7 PG3
John Williams, Head, Mar, 56, Registrar of Births & Deaths, Cheshire Malpas
Arabella do, Wife, do, 47, do wife, do Pargate (probably should be Parkgate)
Alice do, Daur, Unm, 23, Dressmaker, Cheshire Malpas
Robert do, Son, , 21, Gardener, do do
George Fredk do, Son, , 17, Saddler & Apprectice, do do
Edmund Alfred do, Son, 14, Scholar, do do
Arabella Emily do, Daur, -, 8, do, do do
1881 Church St Malpas RG11/2872 ED1 FOL4 PG2
John Williams, Head, Mar, 66, Registrar of Births & Deaths, Cheshire Malpas
Arabella do, Wife, do, 56, do wife, do Parkgate
Alice do, Daur, Unm, 33, Dressmaker, do Malpas
Alfred do, Son, Unm, 23, Grocer's Asst, do do
Emily do, Daur, Unm, 16, Pupil Teacher's, do do
So it appears that this chap was in the habit of being known by his middle name.
